welcome to the fluid mechanics lesson series my name is john zimbala and this is the first lesson in the series lesson 1a introduction in this lesson we'll define fluid mechanics by first defining a fluid and then defining mechanics we'll also discuss normal stresses and shear stresses so what is fluid mechanics it's composed of two words fluid and mechanics so we'll first define a fluid common definition is that a fluid is a liquid or a gas if you think about the three common states of matter solid liquid and gas these two are fluids it turns out that we can often treat these two the same liquids and gases here's the caveat to that if compressibility effects are negligible and there's no free surfaces we mean for example water surface exposed to air then liquids and gases behave the same so we can analyze just a fluid without worrying about whether it's a gas or a liquid liquids and gases behave pretty much the same here's some quick examples some students at penn state built a human powered submarine but we tested it in my wind tunnel another example i was studying some jet engine exhaust for research project and i tested it in a water tunnel so if we compare the actual fluid and the test fluid the actual fluid here was water but the test fluid was air in this case the actual fluid was air and the tested fluid was water it's just a matter of convenience in water it's easier to visualize in an air it's easier to measure as i mentioned up here these are the exceptions liquids with the free surface and gases in high speed flow for free surface effects this would for example be waves generated by a boat on the surface of a lake gases in high speed flow would be for example rockets where compressibility effects are significant you can't model this case with air and you can't model this case with water here's a formal definition of a fluid a fluid is a substance that deforms continuously under the application of a shear stress well we can't understand that unless we know what a stress is in particular what a shear stress is here's a definition of stress stress is a force per unit area acting on a surface we have both normal stresses and shear stresses let's look at a solid object and a liquid of course the liquid has to be in a container of some kind in both cases we add a normal stress a normal stress by its definition is normal in other words 90 degrees to the surface on which it acts what happens when we add a normal stress on this solid in other words we just push down on it well the solid will deform probably something like this it'll bulge out and it'll press down a little bit and then it sits still under this new condition we can also add a normal stress to the liquid by imagining a piston on the surface of the liquid and we push down on it assuming this is a rigid container liquid can't bulge out but it can compress a little liquids are approximately incompressible meaning that they don't compress very much in fact we'll assume that liquids are incompressible in this course we can write this statement a solid can resist a normal stress it deforms but it resists that normal stress for the liquid we have to add the caveat a liquid at rest can resist a normal stress so both a solid and a liquid at rest can resist a normal stress pressure is the most common example of a normal stress in fact in a fluid at rest the only normal stress is the pressure stress and pressure always acts inward and normal to a surface for example if you have a solid object like this the pressure acts always inward and normal always acts towards the surface and normal to the surface this is the case of an actual surface like a potato the same thing applies however to an imaginary surface if we have a fluid particle the same shape as this potato but it's in air we can draw an imaginary surface around that object this fluid particle the pressure will still act normal and inward we can call this a fluid particle which is just a chunk of fluid with imaginary boundaries well these are normal stresses what about shear stresses let's do the same kind of comparison between the solid and the liquid a shear stress is a tangential stress on a surface so if we apply a tangential stress a shear stress on the solid assuming this part is anchored to the ground it will distort somewhat i'm exaggerating here it will distort something like this and as long as we keep applying that stress it'll just sit there in this new configuration so we say that a solid can resist a shear stress what happens if we try the same thing on a liquid we apply a shear stress at this free surface of the liquid again the container can't distort but the liquid will start moving in fact it'll set up some kind of a recirculating pattern so it sets up a flow internally in this container in other words fluid cannot resist shear stress it deforms continuously when you apply a shear stress and deforming continuously means that it sets up some kind of a flow so to make this more correct we need to say a fluid at rest cannot resist the shear stress and that's the bottom line of what we wrote here fluid at rest cannot resist a shear stress instead it will deform and flow in contrast the fluid in motion can have both the shear stress and a normal stress let's look at our solid and our liquid again when we apply a shear stress to the solid there will be stresses on this little element of the solid let's examine all the stresses on this solid element and on the liquid element using a free body diagram let's magnify the element since this solid has distorted there are shear stresses and normal stresses on it the shear stress on this element will look like that and there will be another one on the bottom that's equal and opposite to keep this thing from spinning infinitely around it has to have balancing stresses on the sides there will also be a normal stress in this case at the top and bottom perhaps a little bit on the sides and there also will be a weight w acting down by the way this is called a body force and these are called surface forces i'll also draw the normal stresses on the sides of this element since this solid is at rest newton's first law tells us that sigma f must equal zero this is statics now consider the liquid first let's add a normal stress since this liquid is at rest it cannot resist a shear stress but it can resist a normal stress so we expect there to be normal stresses like this but no shear stresses there also will be a weight associated with this little element due to gravity we'll get into this later with hydrostatics but the pressure at the bottom has to be bigger than the pressure at the top in order for this thing to stay still again this is statics so sigma f has to equal 0. since this liquid element is at rest only normal stresses are possible as we have drawn now let's look at this liquid with shear added i'll resketch this now suppose all we do is add our shear stress at the surface now our fluid particle will not stay still it will move and our free body diagram has to have both normal stresses and shear stresses as well as weight but in this case the fluid particle is not just sitting still but it's moving in fact if it's moving in some kind of curved path it has to have acceleration so our equation now is sigma f equal ma newton's second law since the fluid particle is accelerating there's a further complication with fluids compared to solids and that is that as this fluid particle moves it also distorts as sketched here it doesn't remain a rectangle but it changes to some other shape and as it keeps moving it will keep distorting to some new shape now to make this a little more realistic if this is an incompressible fluid the area in all three of these must be the same since it's not compressing if you had a compressible gas not only will it change shape but it can also compress and get smaller or decompress and get larger in both cases they distort finally let's return to our definition of fluid mechanics we defined fluid now we have to define mechanics so what is mechanics the dictionary says mechanics is the application of the laws of force and motion and then it goes on to say there are two branches statics and dynamics so in this course we'll study both fluid statics which is also called hydrostatics and this is the study of fluids at rest we'll make use of free body diagrams as we did above when everything is at rest we have sigma f equals zero fluid dynamics is the study of fluids in motion fluid mechanics is both or either fluid statics or fluid dynamics when you have fluid dynamics fluids in motion then you have acceleration and we must use sigma f equal ma instead of zero so finally combining these two definitions fluid mechanics is the application of the laws of force and motion on a fluid which is a substance that deforms continuously under the application of a shear stress and the two branches are fluid statics and fluid dynamics